QUANTITATIVE FINANCE RESEARCH PORTFOLIO

Applied Mathematics, Statistics & Numerical Methods Applied to Quantitative Finance

Travis is an Applied Mathematics and Statistics student building rigorous quantitative models for interest rates, derivatives, macro regimes, and risk management. This site contains interactive research, financial models, numerical methods, Python projects, and C++ implementations.

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Python · NumPy · SciPyC++ · Monte Carlo · PDEFixed Income · DerivativesCanadian Rates & Macro

RESEARCH WORKFLOW

Data

Mathematical Model

Numerical Method

Signal

Scenario / Action

Risk

Result

QUANTITATIVE PROJECTS

All projects

CAD Yield Curve & Rates Engine

Government of Canada yield curves with bootstrapping, Nelson-Siegel calibration, PCA, DV01, duration, convexity, and interest-rate scenario analysis.

PythonFixed IncomeNumPySciPy

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C++ Derivatives Pricing Engine

Black-Scholes, Monte Carlo simulation, binomial trees, finite-difference PDE methods, Newton-Raphson implied volatility, and Greeks with numerical convergence comparisons.

C++DerivativesMonte CarloPDE

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Canadian Macro Regime Model

Inflation, GDP, BoC rates, oil, and CAD modelled with Kalman filters, hidden Markov models, and time-series econometrics for regime detection.

PythonMacroKalman FilterHMM

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XVA & Counterparty Risk Simulator

Monte Carlo exposure simulation, expected exposure, PFE, CVA, default probability, recovery rates, and collateral for counterparty credit risk.

PythonMonte CarloCVARisk

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Cross-Asset Macro Stress Engine

Multi-asset stress testing across rates, equities, FX, and commodities with VaR, Expected Shortfall, factor risk, and portfolio optimization.

PythonVaRPortfolioStress Testing

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Stochastic Processes & SDE Lab

Brownian motion, GBM, Ornstein–Uhlenbeck, Vasicek, CIR, and Heston stochastic volatility with Euler–Maruyama and Milstein discretization and Monte Carlo moment validation.

PythonStochastic CalculusMonte CarloHeston

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TECHNICAL SKILLS

Python

NumPy

pandas

SciPy

statsmodels

scikit-learn

FastAPI

C++

Numerical algorithms

Monte Carlo simulation

Optimization routines

PDE solvers

High-performance computation

Mathematics

Probability & statistics

Linear algebra

Optimization

ODEs & finite differences

Approximation theory

Fourier methods

Conjugate gradient methods

Numerical analysis

ABOUT

Travis is an Applied Mathematics and Statistics student applying rigorous mathematical and computational methods to financial markets. His focus spans Canadian interest rates, macro regime modelling, derivatives pricing, and quantitative risk management — with implementations in Python and C++.